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arXiv · 1806.02261

Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with $\beta$-Divergences

Jeremias Knoblauch·Jack Jewson·Theodoros Damoulas
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Abstract

We present the very first robust Bayesian Online Changepoint Detection algorithm through General Bayesian Inference (GBI) with $\beta$-divergences. The resulting inference procedure is doubly robust for both the parameter and the changepoint (CP) posterior, with linear time and constant space complexity. We provide a construction for exponential models and demonstrate it on the Bayesian Linear Regression model. In so doing, we make two additional contributions: Firstly, we make GBI scalable using Structural Variational approximations that are exact as $\beta \to 0$. Secondly, we give a principled way of choosing the divergence parameter $\beta$ by minimizing expected predictive loss on-line. Reducing False Discovery Rates of CPs from more than 90% to 0% on real world data, this offers the state of the art.

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Jeremias Knoblauch, Jack Jewson, Theodoros Damoulas. 2018-06-06. Doubly Robust Bayesian Inference for Non-Stationary Streaming Data with $\beta$-Divergences. https://arxiv.org/abs/1806.02261

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